Abstract:We give a systematic construction of semiorthogonal decompositions of derived categories of coherent sheaves on quasi-smooth derived algebraic stacks over $\mathbb{C}$, where the summands are subcategories defined by weight conditions, and the inclusion functors are given by parabolic induction. The summands are indexed by the component lattice of the stack, a central combinatorial structure in intrinsic Donaldson-Thomas theory. As examples, we obtain semiorthogonal decompositions for moduli stacks of semistable $G$-bundles or $G$-Higgs bundles on a curve, and moduli stacks of de Rham or Betti $G$-local systems on a curve, for reductive groups $G$ not necessarily of type A.
| Comments: | 64 pages |
| Subjects: | Algebraic Geometry (math.AG); Representation Theory (math.RT) |
| Cite as: | arXiv:2605.25976 [math.AG] |
| (or arXiv:2605.25976v1 [math.AG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25976 arXiv-issued DOI via DataCite (pending registration) |
From: Chenjing Bu [view email]
[v1]
Mon, 25 May 2026 15:50:11 UTC (68 KB)
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